A particle of mass 
falls from rest through a resistive medium having resistive force, 
, where 
is the velocity of the particle and 
is a constant. Which of the following graphs represents velocity ( 
) versus time ( 
)?
Text Solution
Verified by ExpertsA
The particle experiences downward gravitational force (mg) and upward resistive force (-kv).
The equation of motion is 
.
Initially at 
gives maximum acceleration 
.
As velocity increases, the resistive force increases, reducing the net acceleration.
Eventually the particle reaches terminal velocity 
when acceleration becomes zero.
The velocity-time graph shows an increasing curve starting from origin with decreasing slope, asymptotically approaching the terminal velocity.
This behavior matches option , which displays a curve starting at 
with steep initial slope that gradually flattens.
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